Answering this without diagrams is going to be hard.....
There are two sorts of polar stereo/grid problems you are likely to encounter. The easiest is the type found in Operational Procedures which talks of convergence as 'east' or 'west'. You can work true to grid or grid to true using a rhyme.
'convergence east true track least,
convergence west true track best'
Where 'best' means 'bigger'
For instance:
The true track at 134ºW is 305º, the convergence is 90ºE, what is the grid track?
So we say 'convergence east true track least' which means grid is bigger so the grid track is 305º + 90º = 395º. This is more than 360 having passed through north so we subtract the 360 to find grid track is 035º
The second sort of problem demands a diagram. A useful convention is to draw northern hemisphere diagrams as a circle with the greenwich meridian at the 6 o'clock position and southern hemisphere diagrams as a circle with greenwich at the 12 o'clock position. This means that easterly longitudes are always on the right and westerly longitudes on the left, just like a normal map.
For instance:
A straight line track is drawn on a polar stereographic chart from A (80ºN 120ºW) to B (80ºN 150ºE). Is the line easterly or westerly at its mid point and what is the initial track at 120ºW?
Draw a northern hemisphere diagram as described above with greenwich at the 6 o'clock. Put in the two positions. A has a westerly longitude so its on the left at about the 10 o'clock position, B is easterly on the right at about 1 o'clock. Draw a line from A to B. Mark the track direction on the line with an arrow.
Identify the half way position roughly, it should be about 11 o'clock. At that point draw a line with an arrow on it pointing to the middle of the circle as a north reference.
Now turn the piece of paper round until the north reference you have just drawn is pointing straight up the page with A on the right and B on the left. The track runs right to left. On a normal map this would be westerly, as it is here. The answer to the first bit is that the track at the mid-point is 270º.
To answer the second bit draw in a north reference at A. Rotate the paper so that the north reference is pointing straight up the page towards the centre of the circle. Notice the track AB is going up and left, this indicates a big angle, more than 270º. To find out how much more find the convergence between A and the mid point. this will be half the total change of long between A and B, which is 90 ÷ 2 = 45º. The track A to B at is therefore 270 + 45 = 315º.
gibber......drool......